ihez=k0E.

To simplify the discussion, consider media where the two diagonal elements of \({\epsilon }_{\parallel }\)  are equal to each other and also equal to the scalar permeability \(\mu \) . This allows us to write \({\epsilon }_{\parallel }={\epsilon }^{\prime }_{\parallel }+{1}\lambda \)  and \(\mu =\lambda \) , where \({\epsilon }_{\parallel }^{\prime }\)  has zeros on the diagonal. When \({\epsilon }_{\parallel }^{\prime }=0\) , the material is impedance matched (\(\mu =\epsilon =\lambda \) ), and the field behaves as if the distance has been rescaled by a factor of \(\lambda \) . This is a simple example of `transformation optics' [1]}, [2]}. When the impedance matching condition is satisfied, there is a propagating wave with some wave number \(|{k}|\)  for every value of \(\lambda \) , with positive \(\lambda \)  corresponding to positive index media, and negative \(\lambda \)  negative index media. There is thus no `gap' in the \(\lambda \)  spectrum. Through introducing a gyrotropy [3]} parameterized by \(\alpha \)
\({\epsilon }_{\parallel }^{\prime }=\left(\begin{matrix}0&-{\rm i}\alpha (x)\\{\rm i}\alpha (x)&0\end{matrix}\right)\) 
